# When random walkers help solving intriguing integrals

## TL;DR

This paper demonstrates how viewing complex integrals through the lens of random walks reveals their properties, enables generalizations, and derives related identities without explicit calculations.

## Contribution

It introduces a novel random walk framework to analyze and generalize intriguing integrals, providing new insights and identities in mathematical analysis.

## Key findings

- Random walk perspective clarifies integral properties
- Generalizations of integrals are systematically derived
- Related identities are obtained without explicit computation

## Abstract

We revisit a family of integrals that delude intuition, and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent when formulated in the language of random walks. In turn, the random walk view naturally leads to a plethora of nontrivial generalizations, that are worked out. Related complex identities are also derived, without the need of explicit calculation. The crux of our treatment lies in a causality argument where a message that travels at finite speed signals the existence of a boundary.